Section numbers are from the textbook Calculus Adams & Essex Edition 9.
Lecture 1 (21.07.2025 - Mon): Introduction to the course, Syllabus, Preliminaries, Real numbers (P1), Cartesian coordinates (P2), Quadratic equations (P3), Circles, Ellipses, Parabolas, Hyperbolas, Scaling and shifting of graphs
Lecture 2 (23.07.2025 - Wed): Preliminaries, Functions and graphs (P4), Operations on functions (P5), Polynomials (P6), Euclidean division
Lecture 3 (28.07.2025 - Mon): The notion of limit (1.2), One-sided limits, Informal and formal definitions of limit, Examples and properties of limit, Squeeze theorem, Limits at infinity and infinite limits (1.3),
Lecture 4 (30.07.2025 - Wed): Continuity (1.4), One-sided continuity, Continuous extension, Maximum-minimum theorem, Intermediate value theorem, The notion of derivative (2.2), One-sided derivatives, Derivatives of fundamental functions, Tangent lines, Differentiation rules (2.3), Leibniz rule, Chain rule (2.4)
Lecture 5 (04.08.2025 - Mon): Derivatives of trigonometric functions (2.5), Higher order derivatives (2.6), Mean value theorem (2.8), Rolle's theorem, Fermat's theorem, Increasing and decreasing functions, Implicit differentiation (2.9)
Lecture 6 (06.08.2025 - Wed): Transcendental numbers and functions, Inverse functions, Derivative of a function's inverse (3.1), Exponential and logarithm (3.2), Natural logarithm and exponential (3.3), Logarithmic differentiation
Lecture 7 (11.08.2025 - Mon): Inverses of trigonometric functions and their derivatives (3.5), Indeterminate forms, L’Hospital’s rule (4.3)
Lecture 8 (13.08.2025 - Wed): Extreme values (4.4), Local and absolute maximum and minimum, Critical, singular, end, inflection points, Concavity (4.5), First and second derivative tests, Extreme value problems (4.8)
Lecture 9 (20.08.2025 - Wed): Sigma notation for sums (5.1), Areas as limits of sums (5.2), Riemann sums (upper and lower), Partitions, Integrability, Definite integral (5.3), Properties of definite integrals (5.4)
Lecture 10 (25.08.2025 - Mon): Fundamental theorem of calculus (5.5), Mean value theorem for integrals, Average value or mean of a function, Method of substitution (5.6)
Lecture 11 (27.08.2025 - Wed): Integration by parts (6.1), Partial fraction decomposition of rational functions, Integration of rational functions (6.2)
Lecture 12 (01.09.2025 - Mon): Inverse substitution method (6.3), Improper integrals of type I and type II (6.5), Convergence and divergence of integrals
Lecture 13 (03.09.2025 - Wed): Areas of plane regions (5.7), Volume calculations (7.1), Solids of revolution, Slicing to disks, Closing remarks